Nonadditive triple-dipole interaction in D3h configuration by variational method: Results of a hard-sphere model and a confined model

Abstract

A model calculation is presented for a study of induction energy of three dipoles located at the vertices of an equilateral triangle, with application to rare-gas atoms and heliumlike ions. The model approach is given with parts which can easily be improved. We preferred the variational method which yields the whole energy in one step, contrary to the perturbation method. The trial wave function respects D3h symmetry. The zero-order wave functions of the systems are assumed to have spherical symmetry when located at the vertices of the triangle. Then the induction energy is expressed in terms of the expectation value of the square sum of electron coordinates which can be obtained in different ways and to which it is very sensitive. The expansion of the nonadditive part of induction energy for long-range distances yields Axilrod-Teller's formula. A semiempirical model with confinement of electron clouds is tested on (Li+)3, showing that repulsion lowers the nonadditivity. Rough results can quickly be obtained for qualitative interpretation by semiempirical use of experimental polarizability data, even for large systems.